·
x^3 + y^3
=1
( x+y ) ( x^2 – xy + y^2 ) =
1 (1)
·
x^2.y +
2x.y^2 + y^3 = 2
( x^2 + x.y^2 ) + ( x.y^2 + y^3 ) =2
xy( x+y) + y^2(x+y) =2
(x+y)(xy + y^2 )=2
(2)
Suy ra :
( x+y ) ( x^2 – xy + y^2 ).2 = (x+y)(xy
+ y^2 )
à 2 ( x^2 – xy + y^2 ) =
xy + y^2
à 2x^2 – 2xy + y^2 – xy – y^2 = 0
à
2x^2 -
3xy + y^2 = 0
à
( x^2 -
2xy + y^2 ) + ( x^2 – xy ) = 0
à
( x – y )
^2 + x (x - y) = 0
à
( x - y)
( x-y+x) =0
à
(x – y )
( 2x - y ) = 0
à
/>
/
> x-y = 0
à x=y (*)
2x – y =0 à y=3x (**)
Trường hợp 1 : x-y = 0
Thay (*) v ào (2) ta
co :
(x+y)(xy + y^2 )= 2
-à 2x ( x^2 + x^2) = 2
-à 2x.2x^2 = 2
-à 4x^3=2
à x =
/>
-à y =3x=3.
/>
Trường hợp 2 : 2x – y =0
Thay ( **) vào (2)
-à ( x+y ) ( x^2 – xy + y^2 ) = 1
à ( x+2x)( x^2 – x.2x + ( 2x)^2) =1
à
3x ( x^2
– 2.x^2 + 4 x^2 ) =1
à
3x .
3.x^2 =1 -à 9.x^3=1 à x =
/>
-à y=3x=3.
/>
ent:.5in'>
·
x^3 + y^3
=1
( x+y ) ( x^2 – xy + y^2 ) =
1 (1)
·
x^2.y +
2x.y^2 + y^3 = 2
( x^2 + x.y^2 ) + ( x.y^2 + y^3 ) =2
xy( x+y) + y^2(x+y) =2
(x+y)(xy + y^2 )=2
(2)
Suy ra :
( x+y ) ( x^2 – xy + y^2 ).2 = (x+y)(xy
+ y^2 )
à 2 ( x^2 – xy + y^2 ) =
xy + y^2
à 2x^2 – 2xy + y^2 – xy – y^2 = 0
à
2x^2 -
3xy + y^2 = 0
à
( x^2 -
2xy + y^2 ) + ( x^2 – xy ) = 0
à
( x – y )
^2 + x (x - y) = 0
à
( x - y)
( x-y+x) =0
à
(x – y )
( 2x - y ) = 0
à
>
> x-y = 0
times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à x=y (*)
2x – y =0 times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à y=3x (**)
Trường hợp 1 : x-y = 0
Thay (*) v ào (2) ta
co :
(x+y)(xy + y^2 )= 2
-times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à 2x ( x^2 + x^2) = 2
-times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à 2x.2x^2 = 2
-times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à 4x^3=2
à x =
>
-times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à y =3x=3.
>
Trường hợp 2 : 2x – y =0
Thay ( **) vào (2)
-times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à ( x+y ) ( x^2 – xy + y^2 ) = 1
à ( x+2x)( x^2 – x.2x + ( 2x)^2) =1
à
3x ( x^2
– 2.x^2 + 4 x^2 ) =1
à
3x .
3.x^2 =1 -times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à 9.x^3=1 times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à x =
>
-times="" new="" roman";mso-hansi-font-family:"times="" roman";="" mso-char-type:symbol;mso-symbol-font-family:wingdings"="">à y=3x=3.
>